Hullo all, Can someone explain the following behavior to me? I would like to to create an extension of the field of rational functions in one variable 'y' over the finite field of three elements by adjoining a root of unity 'Y' and an element of Carlitz torsion 'X'.
I run the following commands: sage: A.<y> = GF(3)[]; A sage: w = polygen(A) sage: K = Frac(A);K sage: A1.<X> = K.extension(w^8 + (y^3 + y + 2)*w^2 + (y^2 + 2*y + 2)); A1 sage: B1.<Y> = A1.extension(w^2+2*w+2); B1 Note that 'w^2+2*w+2' is irreducible over GF(3), and 'w^8 + (y^3 + y + 2)*w^2 + (y^2 + 2*y + 2)' is irreducible over 'A'. All fields are generated successfully. Trying to multiply 'X' and 'Y' or even 'y' and 'Y' then yields a NotImplementedError. This seems crazy to me, since by the output for 'B1', it knows it is an extension of 'A1', but it gets crazier. If instead I restart my worksheet and run: sage: A.<y> = GF(3)[]; A sage: w = polygen(A) sage: K = Frac(A);K sage: A1.<X> = K.extension(w^9 + (y^3 + y + 2)*w^3 + (y^2 + 2*y + 2)*w); A1 sage: B1.<Y> = A1.extension(w^2+2*w+2); B1 where I have multiplied through by 'w' in the modulus of 'A1', the extensions are generated correctly, and one may do arithmetic in all variables 'X', 'Y', and 'y'. I already have a workaround, but this behavior seems like a bug. So I thought I would ask. What's going on here? All the best, Rudy -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
